/sci/ - Science & Math » Thread #12055895

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Anonymous Thu 27 Aug 22:31:57 2020 No.12055895 View Reply Original Report

Quoted By: >>12055910

why is i special? hear me out
you could try introduce other inconsistencies in math by adding new symbols. fr example 1/0 = u.
then you end up with the logic of pic related.
why doesnt introducing i cause similar problems for the basic rules of algebra?

Anonymous

Anonymous Thu 27 Aug 2020 22:37:05 No.12055910 Report

Quoted By: >>12055926

>>12055895
Because imaginary number system is consistent, you can't define 1/0 = u because its logically undefinable, which is why its undefined.

Anonymous

Anonymous Thu 27 Aug 2020 22:42:32 No.12055926 Report

Quoted By: >>12056437

>>12055910
yes, but why is it consistent. sqr -1 doesnt exist after all.

Anonymous

Anonymous Fri 28 Aug 2020 02:33:46 No.12056437 Report

Quoted By:

>>12055926
You can actually make up any new number which is the root of a polynomial and nothing will break (you still have a field). For example you can append sqrt2 to the rationals by making up a number which solves x^2 - 2 = 0. You get i from the reals by making up a number which solves x^2 + 1 = 0. The problem with 1/0 is that it is not the root of any polynomial.

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